On a hot dry day the temperature is high and the watervapour holding capacity of the air is also high ,thus evaporation takes place. The water in the cooler evaporates taking the enrgy from its surronding and hence it leaves the surrounding cool too. This is the reason why a desert cooler cools better on a hot dry day....

In a desert cooler, the water inside it is made to evaporate. This leads to absorption of energy from the surroundings, thereby cooling the surroundings. Again, we know that evaporation depends on the amount of water vapour present in air (humidity). If the amount of water vapour present in air is less, then evaporation is more. On a hot dry day, the amount of water vapour present in air is less. Thus, water present inside the desert cooler evaporates more, thereby cooling the surroundings more. That is why a desert cooler cools better on a hot dry day.